The two leaders called the strikes an "attack on Iraqi sovereignty" and called for national unity, according to a statement cited by Iraq's state news agency.

The strikes took place near the border with Syria, said a statement on Sunday from the Popular Mobilisation Forces (PMF), a state umbrella grouping of mostly Iran-backed Shi'ite Muslim factions.

The PMF said two unmanned aircraft had carried out the attacks, killing one fighter and seriously wounding another. It accused the United States of providing air support to Israel for the strikes.

A security source told Reuters there were two air strikes, one of which struck the headquarters of a local paramilitary brigade, while the other struck a convoy of cars leaving the building.

The attack happened after a series of explosions in recent weeks at weapons depots belonging to PMF groups.

In a statement on Monday, the Pentagon said its forces did not conduct the attack on the convoy or recent attacks on ammunition storage facilities. It did not address whether the United States provided air support.

"We support Iraqi sovereignty and have repeatedly spoken out against any potential actions by external actors inciting violence in Iraq," it said.

The Pentagon said it was cooperating with an Iraqi investigation of the attacks.

"We are operating - not just if needed, we are operating in many areas against a state that wants to annihilate us. Of course I gave the security forces a free hand and instructed them to do anything necessary to thwart Iran’s plans," he said. (Reporting by John Davison and Samar Hassan; Additional reporting by Eric Beech in Washington; Editing by Deepa Babington and Peter Cooney)